The Welfare Cost of Monetary Policy Loss after the Euro Adoption in Poland.

Transcription

1 The Welfare Cost of Monetary Policy Loss after the Euro Adoption in Poland. Michaª Gradzewicz Krzysztof Makarski October 28 Abstract One of the most important aspects associated with the Eurozone accession of Poland is the macroeconomic impact of the loss of autonomous monetary policy. In order to analyze this issue, we build a two country DSGE model with sticky prices. We begin by evaluating performance of our model. Next, we investigate how joining the Eurozone will aect the business cycle behavior of the main macroeconomic variables in Poland. We nd that the Euro adoption will have a noticeable impact on the Polish economic uctuations. In particular, volatility of domestic output increases and volatility of ination decreases. Also, in order to quantify the eect of the Euro adoption, we compute the welfare eect of this monetary policy change. Our ndings suggest that the welfare cost is not large. 1 Introduction After accession to the European Union in 24, Poland, as well as the other New Member States, is going to adopt the Euro as a national currency and become a member of the Euro area. However, the accession to the Euro area implies important changes in both The views expressed herein are those of the authors and not necessarily those of the National Bank of Poland or any other individual within the NBP. The paper presents the results of the research conducted as a part of the process of preparing the Report on Poland's membership of the euro-area. The project serves as a supporting study for the Report and, consequently, its ndings do not determine the overall conclusions of the Report. We wish to thank the participants of the BISE seminars and the anonymous referee for helpful comments and suggestions. Economic Institute, National Bank of Poland Economic Institute, National Bank of Poland and Warsaw School of Economics 1

2 macroeconomic policy and behavior of the accessing economy. The most important of these are: xing of the exchange rate against the other participants of the Euro area, resignation from the autonomous monetary policy in favor of the common monetary policy conducted by the ECB. The consequence of these changes generate additional benets for the accessing country, but they may also induce additional costs to the economy. To a large extent, the existing literature focused on welfare benets associated with the membership in the monetary union. Rose (2) and Frankel and Rose (22) argued that accession to the monetary union boosts trade, creating welfare gains. But their estimate of the magnitude of this eect met some criticism - see e.g. Faruqee (24). In case of the Polish economy, the important contribution of Daras and Hagemejer (28) shows the benets of the Euro adoption, taking into account the trade creation aect and a decline of a long-term real interest rate through elimination of the risk premium. Their results were calculated using dynamic Computable General Equilibrium model (CGE) framework. Our contribution to the discussion on the consequences of Euro adoption concentrates on the costs associated with abandoning the autonomous monetary policy. So, after accession to the Euro area monetary policy will be conducted by the European Central Bank and will be responding, in the rst place, to the events aecting the whole Euro area. In the presence of asymmetric shocks, aecting mainly a given member country, the common monetary policy will be less suited to the current situation of this country, giving rise to additional volatility of economic development and associated costs of these uctuations. Thus, our analysis aims at assessing the impact of resignation from autonomous monetary policy on the volatility of economic development, measured by a set of main macroeconomic indicators. We are also going to provide an estimate of the welfare costs associated with the monetary policy change. In order to perform this calculation, we propose a Dynamic Stochastic General Equilibrium model (DSGE 1 ) of two economies (Poland and the Euro area) linked through trade in goods and services and incomplete international assets market. In order to specify properly the parameters of the model, we decided to estimate a relatively large number of parameters on the basis of the data from both economies. It allows us to develop a model that mimics closely the behavior of both economies. 1 This framework builds on the seminal paper of Kydland and Prescott (1982) and the Real Business Cycle school, which was enhanced with Keynesian-type of nominal rigidities, like in the important work of Smets and Wouters (23), resulting in neoclassical synthesis - see e.g. Goodfriend and King (1998). 2

3 The DSGE methodology is relatively well suited to analyze the consequences of monetary policy regime switch. The model describes the laws of motion of the economy which are derived from microeconomic foundations. In other words, all agents populating the economy solve well specied decision problems and respond in an optimal way to changes in economic environment. As the economy is described in terms of preferences, technologies and the rules of market clearing, the model is parametrized in terms of so called deep parameters. It implies that these parameters are invariant to changes in policies and changing environment and it is possible to analyze the consequences of these changes in a way that is immune to the Lucas critique (see Lucas, 1976). Additionally, agents populating the economy, while making their decisions, form expectations (under the assumption on rationality) about future path of economic development, so the model incorporates expectations in an internally coherent way. All these features make the DSGE framework a parsimonious tool to analyze the consequences of resignation from the autonomous monetary policy in Poland. According to the standard economic theory, monetary policy is neutral in the long run, so the change of the monetary policy regime should not aect the economy in the long run. Thus the monetary policy regime change should inuence the volatility of the economy, rather than the level of economic development. As households are usually assumed to be risk averse, they dislike high variation in incomes and consumption, thus higher volatility of economic growth generates the welfare costs for households. Since households preferences are directly specied in the DSGE framework, we are able to assess the consequences of Euro adoption not only in terms of volatility of economic growth (as in Karam, Laxton, Rose, and Tamirisa (28)), but also in terms of welfare (as in Lucas, 1987). Our approach is directly related to the literature on the costs of business cycle uctuations, which starts from the seminal contribution of Lucas (1987). Lucas nds that the costs of economic uctuations are very small - his estimate for the US economy implies that individuals would sacrice at most.1% of lifetime consumption (his point estimate under reasonable calibration of the prototype economy amounts to.8%). The result of Lucas was quite controversial and launched subsequent research. Barlevy (24a) reviews the literature on this topic and nds that the literature nds the costs of business cycles ranging from.1% to 2% of lifetime consumption. The higher estimates are usually obtained with either non-standard preferences (e.g. Epstein-Zin) or high risk aversion (calibrated to match household micro data, which is inconsistent with the macro evidence for the class of CRRA preferences). The standard models of the business cycle uctuations generate relatively low estimates of the business cycle costs due to two considerations. On the one hand, when thinking about uctuations one is usually thinking of recessions, as times when people are worse o, but the lack of economic uctuations also means that there are no economic expansions - the long 3

4 periods when individuals are actually better o. On the other hand, economic uctuations in a DSGE models are optimal responses of economic agents to changes in the economic environment. If these are optimal, so it is relatively hard to make people much more happy without uctuations. Additionally, the standard models of business cycle uctuations imply that there are no long-run consequences of these, so there are no level eect of uctuations (and thus the magnitude of the welfare loses is of the second order). There is also a literature that argues that there is the level eect. The so called endogenous business cycle literature (see e.g. Barlevy, 24b) assumes that there are long run eects of economic uctuations, so uctuations have the level eect on welfare, which results in much higher costs of cyclical uctuations - an order of magnitude higher, like 8% in Barlevy (24b). This approach builds mainly on the empirical evidence showing that higher volatility of economic growth is usually associated with lower average growth rates. But the tools of this approach are mostly econometric, thus the causality still remains unsolved. As far as we know there does not exist a general equilibrium model incorporating these relationship, which is well grounded in the data. Due to this shortcoming and the fact that literature on endogenous cycle is not in the mainstream of economic thinking, we choose the rst approach to the business cycle. The literature on the costs of the Euro adoption (or more broadly - monetary union) is rather limited. Ca' Zorzi, De Santis, and Zampolli (25) argue that adopting the Euro is more likely to be welfare enhancing the higher the relative volatility of supply shocks across the participating countries, the smaller the correlation of countries' supply shocks and the larger the variance of real exchange rate shocks. Additionally, the welfare eects do not depend on deterministic factors inuencing the real exchange rate (such as Balassa- Samuelson eect), but rather on variances and covariances of shocks. They also claim, that the Euro area accession decreases the eectiveness of the monetary policy response to the stochastic shocks, so it creates a cost of monetary union. However, the Euro adoption could be benecial if the positive inuence on potential output (through the trade creation channel) is higher than the negative eect of lower monetary policy eectiveness. Karam, Laxton, Rose, and Tamirisa (28) use a DSGE model developed in IMF to assess the implications of Euro adoption on the volatility of an accessing country (the model is roughly calibrated to data from the Czech Republic - the authors argue that it is a typical New Member economy 2 ). Their results show that the accession of a small country to the Euro area increases volatility of both ination and output, as the exchange rate no longer 2 This argument is very stylized as there are many features that distinguish Eastern European countries, especially in terms of volatility of GDP components - for some discussion, see Choueiri, Murgasova, and Székely (25). 4

5 buers a part of the volatility generated by economic shocks 3. The increase of the volatility of economic uctuations gets smaller with the ercer competition in the goods market, the smaller rigidities and the greater trade integration with the Euro area. The approach of Karam, Laxton, Rose, and Tamirisa (28) provides many interesting answers, although it focuses on the volatility eects of Euro adoption, emphasizing the ination-output volatility faced by the central bank. They do not try to quantify the welfare results of the Euro area accession. Lopes (27) uses a framework that is the most closely related to ours. She also uses a symmetric two-country DSGE model, with capital and nominal rigidities 4, but she calibrates all of the model parameters. The latter is relatively hard in case of New Member States as the research on technologies, preferences and market structures in these economies is rather scarce. She nds the welfare costs of loosing monetary policy independence of.25%of lifetime consumption (in case of Poland). We believe that her result might be biased, since it is based only on one draw of random shocks for about 1 periods and our experiments show that one needs a large number of draws to for convergence of the welfare result. She also points into the existence of the level eects, which in our computations disappear as the number of draws increases. The rest of the paper is organized as follows. Next section discusses the model we are going to use in order to assess the consequences of loosing monetary policy independence. Then we discuss calibration and estimation issues and show the performance of the model, both in terms of impulse response functions and moments of the model variables against the data. Next, we present and discuss the results of the model both in terms of volatilities of economic aggregates, as well as in terms of welfare. Then we conclude the paper. 2 Model We employ the standard dynamic general equilibrium model of business cycle with nominal rigidities. In our model, monopolistic producers set prices in a style proposed by Calvo (1983). We build a two country model in the tradition of Chari, Kehoe, and McGrattan (22). In the model we call Poland the home country and Eurozone the foreign country. 3 The authors argue that...exible exchange rate plays an important buering role that facilitates macroeconomic adjustment to shocks in small, emerging economies, which allows the central bank to achieve better outcomes in terms of domestic volatility. In general, the results show that there is a cost to a small, emerging economy in joining a common currency area when this exibility is lost. The essential reason is that there are rigidities in domestic adjustment, and when the burden of macroeconomic adjustment is forced onto domestic nominal variables under the common currency, macroeconomic volatility generally increases... - Karam, Laxton, Rose, and Tamirisa (28), page Although she uses the staggered price setting in the spirit of Taylor (198) and we choose a framework of Calvo (1983), that is more frequently used in the DSGE literature. 5

6 Monetary policy is modeled as an interest rate rule similar to the one proposed by Taylor (1993). Our model shares many features with closed economy models (including Erceg, Henderson, and Levin (2), Smets and Wouters (23)), or small open macro economy models (including, Altig, Christiano, Eichenbaum, and Linde (25), Christiano, Eichenbaum, and Evans (25), Adolfson, Laséen, Lindé, and Villani (25)), or other two country models (including Lopes (27) and Rabanal and Tuesta (27)). Households can save in domestic bonds and/or international bonds. We assume that domestic bonds markets are complete but international bonds markets are incomplete. Introduction of this market structure leads to the arbitrage condition that after log-linearized version takes a form of the uncovered interest rate parity (UIP) condition. Households also decide how much capital to rent to producers (utilization rate) and choose how much to invest in new capital. Furthermore, households supply labor in the competitive labor market. There are three stages of the production process. In the rst stage producers oer differentiated products to both domestic and foreign second stage producers. They set their prices according to the Calvo scheme. By including the nominal rigidities in the buyer's currency, we obtain the incomplete exchange rate pass-through. In the remaining two stages, perfectly competitive producers combine those dierentiated goods into a single consumption/investment good with domestic and foreign component. Next, we describe in detail the optimization problems of consumers and producers as well as the behavior of scal and monetary authorities. 2.1 Households There is a continuum of households of measure 1. The fraction ω of households reside in home country and the fraction 1 ω of households reside in the foreign country. Households choose consumption level, as well as their labor supply, domestic bonds holdings (complete markets), international bonds holdings (incomplete markets). They also choose the capital utilization rate and the investment level. The representative domestic household's preferences are of the form 5 [ ] W = E β t u(c t, l t, ζ t ), (1) t= 5 The convention employed in this paper is that asterisk denotes the counterpart in the foreign country of a variable in the home country (for example c t is consumption in the home country, and c t is consumption in the foreign country). The same applies to the model's parameters. Whenever we see potential for confusion we explicitly clarify notation. 6

7 where c t and l t denote the representative household's level of consumption and labor supply, respectively. ζ t denotes the labor supply shock that follows AR(1) process ˆζ t = ρ ζˆζt 1 + ε ζ,t, (2) where E t [ζ t ] = 1 and ˆζ t = ζ t 1 (in the steady state ζ = 1). Throughout the whole paper we assume the following form of the instantaneous utility function u(c t, l t, ζ t ) = c1 σ t 1 σ ψζ t l 1+γ t 1 + γ. (3) We restrict our analysis to the case of a representative consumer by assuming complete domestic nancial markets. In period t there is a complete set of state contingent one-period nominal bonds B t+1, each worth Υ t,t+1. Households can also trade bonds with abroad. We assume that there is one, internationally traded, uncontingent nominal bond, nominated in foreign currency Dt+1 (denote home country holdings of this bond as DH,t+1, and foreign country holdings of this bond as DF,t+1 ). From the point of view of the home country the interest rate on this bond is Rt κ t, where κ t denotes risk premium. The risk premium is a function of the domestic debt (as in Schmitt-Grohe and Uribe (23)) ( ( et D )) H,t+1 κ t = exp χ d ɛ κ,t, (4) P t GDP t where e t, P t and GDP t denote the nominal exchange rate, the price of the consumption good and GDP, respectively. The constand d is calibrate so as there is no risk premium in the steady state. ɛ κ,t denotes the risk premium shock that follows AR(1) process ˆɛ κ,t = ρ κˆɛ κ,t 1 + ε ζ,t, (5) where E t [ɛ t ] = 1 and ˆɛ t = (ɛ t 1)/1 (in the steady state ε = 1). Moreover, households own the capital stock. The dynamics of the physical stock follows the law of motion k t+1 = (1 δ) k t + ( ( )) xt 1 S x t, (6) x t 1 where k t and x t denote the capital stock and investments. S (x t /x t+1 ) is a function which transforms investments into physical capital. We adopt the specication of Christiano, Eichenbaum, and Evans (25) and assume that S (1) = S (1) =, and ι = 1/S (1) >. Households choose also the capital utilization rate u t, and have to pay the capital utilization rate adjustment costs, according to the following cost function Ψ (u t ), satisfying Ψ (1) =, Ψ (1) > and Ψ (u t ) >. Moreover, households rent capital to producers. Denote the 7

8 capital stock employed by producers as k t, then and the rental rate of capital is denoted r t. All households face the same budget constraint in each period c t + x t + E t [Υ t,t+1 B t+1 ] P t + D H,t+1 e t P t R t κ t = k t = u t kt (7) w t l t + (r t u t Ψ (u t )) k t + B t P t + e td H,t P t T t + Π t, (8) where P t, w t, T t and Π t denote the price of the consumption good, real wage, real lump sum tax and real prots from all producers, respectively. The representative household maximizes (1) subject to the budget constraint (8) (denote the Lagrangian multiplier on budget constraint as λ t ) and the law of motion of capital (6) (denote the Lagrangian multiplier on budget constraint as λ t Q t ). Solving, we get the following rst order conditions c t : β t u c,t = λ t, (9) l t : β t u l,t = λ t w t, (1) ( ) ( ) ) x λ t = λ t Q t (1 S t x t 1 S x t x t x t 1 x [ t 1 x t : ( ) ( ) )] 2 +E t Q t+1 λ t+1 (S xt+1 xt+1 (11) x t, x t k t+1 : E t [λ t+1 (r t+1 u t+1 Ψ (u t+1 ))] = Q t λ t E t [Q t+1 λ t+1 (1 δ)], (12) u t : r t = Ψ (u t ), (13) [ ] λt+1 P t B t+1 : E t [Υ t,t+1 ] = E t, (14) D H,t+1 : 1 R t κ t = E t [ λt+1 λ t λ t P t+1 ] P t e t+1, (15) P t+1 e t and the transversality conditions. Dene the nominal interest rate in home country as The log-linearized equations can be found in Appendix A. 1 R t = E t [Υ t,t+1 ] (16) 8

9 2.2 Producers There are three stages of production process in both economies. Next, we describe the actions of producers in home country, producers in foreign country act analogously. In the last stage nal domestic goods producers buy home and foreign intermediate goods and combine them into domestic consumption/investment goods that are sold to consumers. In the second stage there are two sectors: H and F. In sector H producers buy home country heterogeneous intermediate goods and aggregate it into sector H homogeneous intermediate goods that are sold to the domestic nal goods producers. Similarly in sector F, producers buy foreign country heterogeneous intermediate goods and aggregate them into sector F homogeneous intermediate goods that are sold to domestic nal goods producers. In the rst stage, heterogeneous intermediate goods producers use capital and labor to produce heterogeneous intermediate goods that are sold both in home country and foreign country. Next we describe the problems of producers in home country in more detail. In terms of notation, goods produced at home are subscripted with an H (excluding home county sector F homogeneous intermediate goods which are subscripted with an F ), while those produced abroad are subscripted with an F (excluding foreign country sector H homogeneous intermediate goods which are subscripted with an H). Moreover, goods that are sold to agents in home are not superscripted, while those sold in foreign are superscripted with an asterisk Final Goods Producers Final goods producers operate in a perfectly competitive market. They buy sector H homogeneous intermediate goods Y H,t and sector F homogeneous intermediate goods Y F,t at competitive prices P H,t and P F,t, respectively. They use those goods to produce a nal goods Y t using the following technology Y t = [η µ 1+µ (YH,t ) 1 1+µ + (1 η) µ 1+µ (YF,t ) 1 1+µ ] 1+µ, (17) which are sold to home country consumers. Since markets are competitive producers take prices as given and, in each period t, choose inputs and output to maximize prots given by P t Y t P H,t Y H,t P F,t Y F,t (18) subject to the production function (17). 9

10 Solving the problem in (18) gives the inputs demand functions Y H,t = η ( PH,t Y F,t = (1 η) ) (1+µ) µ P t ( ) (1+µ) PF,t µ P t Y t, (19) Using the zero prot condition, we construct the index of domestic prices P t = Homogeneous Intermediate Goods Producers Y t. (2) ] [(1 η) (P F,t ) 1 µ + η (PH,t ) 1 µ µ. (21) Homogeneous intermediate goods producers in sector d {H, F } operate in a competitive market. Producers in sector H, buy heterogeneous intermediate goods y H (i), i [, 1], produced in home country, while the producers in sector F buy heterogeneous intermediate goods y F (i), i [, 1], produced in foreign country. Prices of these heterogeneous intermediate goods are set in currency of home country, p d,t (i), i [, 1] and d [H, F ]. The technology for producing homogeneous intermediate goods in sector d {H, F } is as follows Y d,t = ( 1 y d,t (i) 1 1+µ d di) 1+µd. (22) Given prices, in each period t, producers choose inputs and output to maximize prots P d,t Y d,t subject to to the production function (22). 1 p d,t (i)y d,t (i)di (23) Solving the producers problem in (23) we obtain the following input demands for heterogeneous intermediate goods ( ) pd,t (i) (1+µ d) µ d y d,t (i) = Y d,t. (24) P d,t From the zero prot condition we also get the price index [ P d,t = p d,t (i) 1 µ d di] µd. (25) 1

11 2.2.3 Heterogeneous Intermediate Goods Producers The technology for producing each heterogeneous intermediate good i [, 1] is the standard constant returns to scale production function y H,t (i) + 1 ω ω y H,t(i) = y t (i) = Ak t (i) α (z t l t (i)) 1 α (26) where k t (i) and l t (i) are the inputs of capital and labor, respectively, while y H (i) and y H (i) are the amounts of the intermediate heterogeneous good i sold in home country and in foreign country 6, respectively. Moreover z t denotes the stationary technology shock that follows an AR(1) process where E t [z t ] = 1 and ẑ t = z t 1 (in the steady state z = 1). ẑ t = ρ z ẑ t 1 + ε z,t, (27) Next we nd the cost function to simplify notationally the prot maximization problem. The cost minimization problem of producer i in period t is c(y t (i)) = min [r tk t (i) + w t l t (i)] (28) k t(i),l t(i) subject to the (26), where r t and w t are the gross nominal rental rate of capital and real wage, respectively. Solving (28) we get the following cost function c(y t (i)) = 1 1 α α (1 α) 1 α (z t ) 1 α rα t wt 1 α y t (i) = mc t y t (i), (29) 1 1 where mc t denotes marginal cost, mc t (y t (i)) = r α α α (1 α) 1 α (z t) 1 α t wt 1 α. Moreover, from the cost minimization problem we get the following condition for the optimal inputs employment ratio r t w t = α l t. (3) 1 α k t The heterogeneous intermediate good i producer sells her products both to home country and foreign country intermediate homogeneous goods producers. Heterogeneity of the intermediate goods, since producers have market power, introduces monopolistic competition, thus it allows us to add the price stickiness to the model. The producers set their prices according to the Calvo scheme. We assume that the prices of heterogeneous intermediate goods are sticky in the buyers currency, which is consistent with the incomplete short term pass-through. Since the marginal cost function is constant in y t (i), we can write down the separate prot maximization problems for goods sold in home country and foreign country. 6 Note that yh,t 1 ω (i) is expressed in per ca pita units of foreign country thus it has to be multiplied by ω. 11

12 In each period, the heterogeneous good i producer, while selling her product in home country y H (i), receives a signal to adjust her price with probability (1 θ H ), otherwise the price evolves according to the following formula p H,t+1 (i) = p H,t (i) π, where π denotes the steady state ination in home country. If the producer receives the signal for price reoptimalization it chooses the reoptimalized price p new H,t (i) and the production level in each period until the next reoptimization {y H,t+j (i)} j= that maximize prots given by the following function E t j ( (1 + τ (βθ H ) j H ) p new H,t Λ t,t+j P t+j (i) πj mc t+j ) y H,t+j (i) (31) subject to the demand function (24), where Λ t,t+j denotes the intertemporal discount factor (consistent with the home country households problem), while τ H denotes production subsidy. Similarly, the same producer, while selling her product in foreign country, in each period with probability (1 θ H) reoptimizes her price and with probability θ H the price evolves according to the following formula p H,t+1 (i) = p H,t (i) π, where π denotes the steady state ination in foreign country. While reoptimizing the producer chooses p new, H,t (i) and { y H,t+j (i) } that maximize the following prot function j= E t j ( (βθ H) j et+j (1 + τ H Λ ) pnew, H,t (i) ( π ) j t,t+j P t+j ) 1 ω ω mc t+j yh,t+j(i) (32) subject to the demand function (24), where e t+j denotes the nominal exchange rate (price of foreign currency in home currency), while τ H denotes production subsidy. Dene the real exchange rate as q t = etp t P t the following rst order conditions E t j E t j ( p (βθ H ) j new H,t Λ t,t+j ( (βθ H) j qt+j p new, H,t ( π ) j Λ t,t+j π t,t+j. Solving the problems (31) and (32) we get (i) πj P t+j 1 + µ H 1 + τ H 1 + µ ) H mc t+j y H,t+j (i) 1 + τ H =, (33) ) 1 ω ω mc t+j y H,t+j(i) =. (34) Thus the producer sets its price so that discounted real marginal revenue is equal to discounted real marginal cost, in expected value. We assume that the subsidy is set to eliminate the monopolistic distortion associated with positive markups, thus for d {H, F } we have τ d = θ d and τ d = θ d. Note that if θ = we obtain the standard condition that price equals marginal cost. The log-linearized equations can be found in Appendix A. 12

13 2.3 Government The government uses lump sum taxes to nance government expenditure and production subsidies. The government's budget constraint in this economy equals G t + 1 τ H p H,t (i)y H,t (i)di + 1 τ F p F,t (i)y F,t (i)di = T t. Since in our framework Ricardian equivalence holds there is no need to introduce government debt. Moreover, we assume that government expenditures are driven by a simple autoregressive process 2.4 Central Bank G t+1 = ( 1 ρ g ) µg + ρ g G t + ε g,t+1. (35) We assume that monetary policy is conducted according to an extended Taylor rule (similar to the one assumed by Smets and Wouters (23)) that targets deviations from the steady state of CPI ination, GDP, growth rate of ination and growth rate of GDP. We also allow for interest rate smoothing R t = where π t = ( Rt 1 R Pt P t 1. ) γr ( (πt 2.5 Market Clearing. π ) ( ) γy ( ) γdgdp ( ) γdπ ) 1 γr γπ GDPt GDPt πt GDP e ϕ t (36) GDP t 1 π t 1 In equilibrium, the goods markets, the assets markets and the production factors markets must clear. The market clearing condition in the nal goods market takes the form c t + x t + G t + Ψ (u t ) = Y t. (37) Note that we have included the market clearing condition in the intermediate goods markets through notation. The market clearing condition in the production factors markets are 1 1 l t (i) = l t k t (i) = k t 13

14 The market clearing condition in the assets markets are B t+1 = B t+1 = and D H,t+1 + D F,t+1 = 2.6 Balance of Payments and GDP Using the market clearing conditions and the budget constraint we get the balance of payments equation q t 1 ω ω P H,t Y H,t P t + e t P t D H,t+1 R t κ t = P F,tY F,t P t + e t 1D H,t P t 1 q t q t 1 π t (38) Furthermore, to close the model, since there is GDP in the Taylor rule we need the formula for GDP, which has the following form GDP t = Y t + 1 ω ω e t P H,t Y H,t P t P F,tY F,t P t (39) The log-linearized equations can be found in Appendix A. 3 Calibration and estimation In order to evaluate the properties of the model against the data describing Polish and the Eurozone economies, we applied a mixture of calibration and estimation procedure. First, we calibrated a subset of parameters that can be easily extracted from the raw data or those resulting from the steady state considerations. Afterwords, we performed a Bayesian estimation of the other parameters, that mainly govern the business cycle volatility of the model. 3.1 Calibration Procedure The calibration of the parameters was based mainly on the data from the quarterly National Accounts, issued either by the Eurostat (in case of the Eurozone 7 ), or by the Polish Central Statistical Oce (GUS). As a measure of exports and imports we used the data from the 7 The Eurozone is dened as EA-15 and includes: Belgium, Cyprus, Denmark, Ireland, Greece, Spain, France, Italy, Luxembourg, Malta, Netherlands, Austria, Portugal, Slovenia and Finland) 14

15 Table 1: The most important calibrated parameters of the model Parameter Value β.99 β.99 δ.17 δ.17 1+µ 2 µ 1+µ 2 µ η.614 η.99 α.33 α.33 Polish National Accounts, then we adjusted the Eurozone data, treating the resulting additional net trade with the rest of the world as government consumption 8. Due to the lack of data on average hours worked, we use employment as a proxy for a measure of labor in the model. We used data on total employment (domestic concept) form the Eurostat in case of Eurozone, and data on employment form the Labor Force Study, in case of Poland. As a measure of wages, we used quarterly data on average wages in the national economy, in case of Poland (due to the lack of data on the compensation of employees for the whole period) and compensation of employees per person employed in case of the Eurozone. The most important calibrated parameters of the model can be found in Table 1. The discount factors β and β were set at the same levels 9 of.99, which implies the annual long-term real interest rate of 4%, consistent with the average real interest rate (3-months interest rate deated by the expected ination, under assumption of a perfect foresight) in the Eurozone for the period Physical capital depreciation rate δ was set at 7% annually in both countries. The elasticity of production with respect to capital, α was set at.33 in both countries, in line with most of the DSGE literature. The inverse of the elasticity (1) of the capital utilization cost function Ψ = Ψ was set at.1, roughly in line with the Ψ (1) estimate in Smets and Wouters (23) (as the data on capacity utilization are hardly reliable and usually cover only manufacturing, we decided not to use them in the estimation step and we calibrated the elasticity from the literature). The long-term ination rate was set at 2.5% annually for both economies. The share of the population of Poland in the total 8 In a a two country framework one need to decide how to deal with the trade with rest of the world. Treating it as government consumption in our framework is relatively nondistortionary, as it only aect the steady state government consumption share and is roughly in line with the approach of Chari, Kehoe, and McGrattan (27). 9 In order to avoid the steady state eects of monetary policy regime change, we used the same discount factor for both economies at set it at the level consistent with the Eurozone. 15

16 population of the Eurozone and Poland, ω was set at.17, on the basis of the data from the Eurostat. The parameters µ and µ were set at 1 in both countries, implying the Armington elasticity of substitution 1+µ µ = 2, consistently with the evidence given by Ruhl (25) and discussion presented in McDaniel and Balistreri (23). The home bias parameters, η and η were set at.614 and.993 respectively, reecting the export to absorption ratio for the period in case of Poland and in case of the Eurozone. The steady state consumption shares (in absorption) were set at.69 and.573 in Poland and the Eurozone, respectively. The corresponding gures for investment shares are.26 and.295. As there is no direct measure of costs of adjusting capacity utilization, in the stead state we set them at 1% of absorption in both countries and treat the government expenditures share as a residual. The absorption to GDP ratio were set at 1.3 and.99 in Poland and the Eurozone. We set the debt share at.46, in line with the average ratio of total external debt of the Polish economy to GDP for the years Some other parameters of the model, that were not estimated were calculated on the basis of the steady-state relations of the model. 3.2 Estimation Procedure All data used in the estimation of the model were expressed in quarterly frequency and adjusted for seasonality (except for the interest rates) using Demetra package and expressed in constant prices of the year 2. As the model does not distinguish between dierent price indicators and monetary policy is aimed at stabilizing consumer price ination, we decided to express all real variables in terms of consumption prices either in Poland or in the Eurozone. We also normalized the variables by the population shares ω and 1 ω in each quarter 1. Then, all variables in logs were detrended using Hodrick-Prescott lter (see Hodrick and Prescott (1997)), with the standard parameter for the quarterly data λ = 16, and expressed as a log-dierence of a given variable and HP-trend, which is consistent with the log-linearization of the model. Our approach was to keep the basic structure of the model relatively simple and to use relatively small number of fundamental stochastic shocks to describe the cyclical uctuations of the economy (we used a technology, a government consumption, a monetary policy and a labor supply 11 shocks for both countries and one risk premium shock). But this approach 1 As there are no consistently measured quarterly data for the Eurozone, we extrapolated the annual data using constant quarterly growth rates within a year, assuring that the data for the beginning of the year are the same as measured by annual data. 11 Especially in case of Poland, it is very hard to model the labor market variables using a relatively simple determination of labor market equilibrium, as in the presented model. So we decided to add a labor supply 16

17 would limit the information that is used in the estimation, as the number of observed variables needs to be equal to the number of stochastic shocks. So, in the estimation of the parameters, we included additional information form other variables, assuming that theory are observed with an iid noise. As primarily variables (observed without noise), we used the following time series for the period IIIQ1996 IV Q27: GDP, government expenditure, consumer price ination, employment for both Poland and the Eurozone, and the interest rate dierential (gross, as in the model denoted as R). The set of additional variables (observed with noise) includes (for both economies): consumption, investments and trade indicators (both exports and imports, expressed in Polish currency). As the model is log-linearized, it can be expressed as a state-space representation and it's likelihood can be evaluated against data via the Kalman lter. We decided to use the Bayesian approach to estimate the model parameters, since it allows to use additional information, that can be provided via the prior distribution of the parameters. The expression for the likelihood function cannot be found analytically, however the posterior distribution of the model parameters can be estimated via Monte Carlo Markov Chain (MCMC) algorithm, proposed by Metropolis and Teller (1953) and Hastings (197). We used the Dynare package in order to solve, estimate and simulate the model (see e.g. Juillard (1996)). After nding the mode of the posterior distribution (using the Chris Sims csminwel procedure that applies a quasi-newton method with BFGS update of the estimated inverse Hessian, robust against "clis", i.e. hyperplane discontinuities) we applied the Metropolis- Hastings MCMC algorithm with 5 replications (to assure that the MCMS algorithm have converged) in two blocks in order to compute the posterior distribution of the model parameter. The acceptation rates were ca. 24%, within the band 23%-25% recommended in the literature. On the basis of the the univariate and multivariate convergence diagnostic of Brooks and Gelman (1998) indicating that the MCMC algorithm converged, we dropped 1% of draws for the purpose of construction of the posterior probability distributions. When choosing the parameters of the prior distributions, we used the results of Smets and Wouters (23), Adolfson, Laséen, Lindé, and Villani (25) and Kolasa (28) and, to some extend, some pre-estimation exercises. The chosen parameters of the prior distribution are presented in Table 2. For most cases we have not distinguished between Poland and the Eurozone, except for ι's, Calvo probabilities θ's and parameters of the Taylor rule. As the installation of the new investments goods in Poland could be more costly, due to more restricted regulations we choose to set lower value for ι than for ι. Also, due to more stringent product market regulations in Poland, we choose to set slightly lower values for θ H and θ F. Additionally, taking into account the results of Kolasa (28), we picked such shock, in order to allow the model to have a chance to describe the labor market behavior in line with the data. 17

18 Table 2: Basic description of the prior and posterior distributions Parameter Prior distribution Posterior distribution type Mean St. Dev. Mode Mean St. Dev. ι norm ι norm γ norm γ norm θ H beta θ F beta θ F beta θ H beta χ norm σ norm σ norm γ R beta γ π norm γ GDP norm γ dπ norm γ dgdp norm γ R beta γ π norm γ GDP norm γ dπ norm γ dgdp norm ρ z beta ρ z beta ρ G beta ρ G beta ρ l beta ρ l beta ρ aκ beta

19 prior distributions of the parameters of the Taylor rule, that the policy rule in the Eurozone is slightly more ination oriented than in Poland. The standard deviations of the stochastic shocks were set on the basis of the pre-estimation exercise. For the standard deviations of the noise components of additional observed variables, we assumed that the noise component variability constitutes 1% of the overall variability of a given variable. 3.3 Parameters The results of the estimation procedure are shown in Table 2. Additionally, we plotted the prior and posterior distributions of all estimated parameters - see Figure 1, including standard deviations of noisy components of additional variables 12. The results of the estimation indicate that our assumption of the relative size of the parameter governing the cost of adjusting capital stock was correct. Also, the additional information from the data have not changed strongly the prior distribution of labor supply elasticity. The estimated coecients of the Calvo parameters indicate that the degree of nominal rigidity in Poland is higher than in the Eurozone, especially in case of goods sold domestically. The estimated Calvo probabilities for the Eurozone are roughly in line with the results of Adolfson, Laséen, Lindé, and Villani (25). The information in data series signicantly changed the estimate of the inverse of the elasticity of intertemporal substitution in Poland - the estimated parameter σ = 3.1 is much higher than the mean of the prior, which was set at 2. The estimated interest rate smoothing coecient in the Taylor rule for Polish economy proved to be lower than expected, γ R =.72, although within the range usually obtained in the literature. Additionally, the responsiveness of the interest to the consumer price ination and GDP is slightly higher than assumed, both in case of Poland and the Eurozone. The estimated degree of interest rate smoothing of the ECB γ R =.77, is slightly lower than the usual estimates (see e.g. Smets and Wouters (23) or Adolfson, Laséen, Lindé, and Villani (25)). The estimated Taylor rule in case of the NBP is as follows: ˆR t =.72 ˆR t 1 + (1.72)[1.29ˆπ t +.46GDP ˆ t +.11dGDP ˆ t +.21dπ ˆ t ] + ϕ t (4) and ˆR t =.77 ˆR t 1 + (1.77)[1.42ˆπ t +.33GDP ˆ t +.9dGDP ˆ t +.21dπ ˆ t ) + ϕ t (41) in case of the ECB. 12 These are the plots of: SE_e_c, SE_e_c_s, SE_e_x, SE_e_x_s, SE_e_import, SE_e_export. 19

20 SE_e_z SE_e_phi_s SE_e_kappa Figure 1: Prior and posterior distributions of the model parameters SE_e_z_s SE_e_phi SE_e_g SE_e_g_s SE_e_c SE_e_c_s SE_e_x SE_e_x_s SE_e_import SE_e_export SE_e_a_l SE_e_a_l_s iota iota_s gamma gamma_s theta_h 1 5 theta_f_s gamma_pi gamma_y 1 5 gamma_dpi theta_f theta_h_s chi gamma_dy gamma_r_s gamma_pi_s sigma sigma_s gamma_r gamma_y_s gamma_dpi_s gamma_dy_s rho_z rho_z_s rho_g rho_g_s 6 4 rho_a_kappa rho_a_l rho_a_l_s

21 The estimated persistence of the technology shocks is very similar in Poland and in the Eurozone, roughly equal to The estimation revealed the the persistence of the government spending shock is much higher in the Eurozone, than in Poland, in line with the economic intuition. Also, the persistence of the labor supply shock proved to be higher in case of Poland, reecting the features of the transforming economy. The persistence of the risk premium shock proved to be relatively small, also in line with the economic intuition 13. The estimated volatilities of the shocks governing the evolution of the economy (not reported in Table 2, but depicted in Figure 1) reveal that the volatility of the technology shock is much larger in Poland, again in line with the economic intuition and in line with the evidence from the relative volatility of output of the Polish economy compared to the Eurozone. The same applies for the monetary policy shock and the labor supply shock. On the other hand, the volatility of the government spending shock is slightly higher in the Eurozone, than in Poland. 3.4 Model's Data Fit In order to evaluate the ability of the model to replicate the features of the data from the Polish and the Eurozone economies, we compared the moments of the model generated variables against the moments of the data. Instead we could have used the theoretical moments of the model's variables, but these describe the large sample properties of the model, whereas when calculating the moments of the data we are using only ca. 5 observations. In order to overcome this issue we decided to simulate the model behavior in short sample. So, we simulated the model using random draws of the stochastic shock 14 for 152 periods and then dropped the rst 1 observations 15, calculating the moments for only 52 observations. We replicated this procedure 1 times (for dierent, independent draws of stochastic shocks) and averaged the resulting correlations in order to assure that our calculated moments are history-independent. Table 3 shows the results of our procedure - the upper panel shows the results for the Polish economy, the lower panel - for the Eurozone economy. The rst two columns show the volatilities of the model generated variables against the data (measured by the standard deviations), the middle two columns show the cyclicality of variables, as measured by correlations with GDP (GDP in case of the Eurozone). The last columns show the persistence 13 Taking into account the relatively fast adjustment and eciency of the exchange rate market, it is not surprising that the agents respond relatively quickly to the exogenous changes in the interest rate disparities. 14 As was mentioned earlier, the additional shocks of the model - noise in additional observables - were used only for the purpose of the estimation, so in the simulations performed on the model, we turned o these shocks. 15 As the simulation starts from the steady state, we dropped some observations to assure that we calculate the moments of variables not being biased by being too close to the steady state. 21

22 Table 3: Moments of the model generated variables against the data Volatility Correlation with GDP Persistence data model data model data model Poland GDP c x π w R l q export import Eurozone GDP c x π w R l

23 of the model generated variables and the data - measured by autocorrelation. The model generates too much volatility of GDP, both in Poland and the Eurozone. The same is true for ination and real wages (and investments in case of the Eurozone economy). The model correctly reproduces, for both economies, the volatility of consumption nominal interest rates and exports. The volatilities of investments in Poland and employment in both economies, as well as imports were underestimated by the model. Our model generates too little comovement with output in case of consumption, investments, employment and imports in case of Poland. The same is true for consumption and employment in case of the Eurozone. The cyclicality of the real exchange rate is largely exaggerated by the model. The model predicts countercyclical ination in the Eurozone, whereas it is slightly procyclical in the data. Also the cyclicality of interest rates are different in the model and data for both economies - in the data interest rates are procyclical (slightly procyclical in case of Poland), whereas the model predicts that monetary policy is countercyclical (the procyclically of interest rates in the data is rather not intuitive and could be an artifact of the short sample used in the analysis). The model reproduces generally well the persistence of analyzed variables - excluding the real exchange rate, exports, and especially ination. Summing up, the model ts the data relatively well, although not perfectly. But taking into account the short sample used in the estimation and evaluation of the model properties, its performance is rather good. The main problems are: exchange rate (even with the equity premium puzzle shock the model cannot generate the properties of this variable, but this is rather common to this kind of methodology - see e.g. Chari, Kehoe, and McGrattan (22)), cyclicality of the interest rates, and cyclicality of ination (the latter in case of the Eurozone). 3.5 Impulse Response Functions In order to understand the dynamic properties of the model, we calculated the impulse response of the model to the most important shocks of the model - asymmetric technology shocks and asymmetric monetary policy shock (that occurred in the Polish economy) Asymmetric Technology Shock After an unanticipated asymmetric technology shock (hitting the Polish economy, see Figure 2) the model predicts the prolonged increase of both consumption and investments, the latter generating the increase of capital stock. The decrease of the domestic prices translates into falling ination and a decline of the nominal interest rates. Real wages decrease on impact, but then quickly rise above the steady state and stay there for a while. The technology shock 23